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March 14th, 2015, 10:16 PM  #1 
Newbie Joined: Nov 2014 From: math Posts: 27 Thanks: 1  Confidence Interval  conceptual understanding
In a randomly selected sample of 500 registered voters in Kowloon, 200 individuals say that they plan to vote for Candidate A in the upcoming election.  If the survey were repeated a lot of times, we expect 90% of the confidence intervals constructed will contain the proportion of all Kowloon voters who plan to vote for Candidate A.  If the survey were repeated a lot of times, we expect 90% of the confidence intervals constructed will contain 40%, which is the estimate of the proportion of Kowloon voters who vote for Candidate A. I think the second statement is right, but I was wrong. Why? What's the difference between the two? 
March 15th, 2015, 01:49 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,834 Thanks: 733 
40% is an estimate of the proportion, but it is not necessarily the true proportion.

March 15th, 2015, 08:27 PM  #3 
Newbie Joined: Nov 2014 From: math Posts: 27 Thanks: 1 
Does that mean when we do the survey many times, it is expected that the intervals we get will be the true proportion?

March 16th, 2015, 03:52 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,834 Thanks: 733 
One of the basic theorems in probability theory is the law of large numbers, which says (essentially) that a sample average converges to the mean as the sample size gets bigger.


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conceptual, confidence, interval, understanding 
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